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From two points, lying on the same horizontal line, the angles of elevation of the top of the pillar are θ and φ (θ < φ). If the height of the pillar is ‘h’ m and the two points lie on the same sides of the piller, then the distance between the two points is
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- h (tanθ – tanφ) metre
- h (cotφ – cotθ) metre
- h (cotθ – cotφ) metre
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h tan θ tan φ metre tan φ tan θ
Correct Option: C
Let AB = height of pole = h metre
∠ACB = θ, ∠ADB = φ
In ∆ABD,
| tan φ = | BD |
| ⇒ BD = | = h cot φ | tan φ |
In ∆ABC,
| tan θ = | BC |
| ⇒ BC = | = h cot θ | tan θ |
∴ Required distance
= CD = h cotθ – h cotφ
= h (cotθ – cotφ) metre
